Journal of Integer Sequences, Vol. 18 (2015), Article 15.6.8

Ménage Numbers and Ménage Permutations

Yiting Li
Department of Mathematics
Brandeis University
415 South Street
Waltham, MA 02453


In this paper, we study the combinatorial structures of straight and ordinary ménage permutations. Based on these structures, we prove four formulas. The first two formulas define a relationship between the ménage numbers and the Catalan numbers. The other two formulas count the ménage permutations by number of cycles.

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(Concerned with sequences A000108 A000179 and A000271.)

Received January 16 2015; revised versions received February 21 2015; June 11 2015; June 15 2015. Published in Journal of Integer Sequences, June 16 2015.

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